School of PE Blog

Curious about Capacitance? Here's What You Should Know

Aug 04, 2023

History

The capacitor is an essential component of modern electronics, but its origins can be traced back to the 18th century. The invention of the capacitor is attributed to the Dutch scientist Pieter van Musschenbroek, who created the first capacitor, also known as the Leyden jar, in 1745.

Musschenbroek's invention was the result of his experiment with static electricity. He discovered that by placing a metal object inside a glass jar filled with water, he could store a charge of static electricity. The jar acted as a capacitor, storing the electrical charge on its metal object (Ho et al., 2010, 1). The Leyden jar was a ground-breaking invention that paved the way for the development of modern capacitors. However, it was not until the 19th century that practical capacitors began to be developed.

In 1839, an English natural philosopher named Michael Faraday discovered that a charge stored in a capacitor is directly proportional to its capacitance and the applied voltage. This discovery laid the groundwork for the development of modern capacitors, increasing its capacitance and reliability.

What Is a Capacitor?

Capacitors come in various sizes, shapes, and capacitances. Sizes can vary from as small as a grain of rice or as enormous as a building. Capacitance is measured in Farads (F), however, most commercial capacitors have values that are small in value. The most commonly used capacitors measure around microfarad (μF) to picofarad (ρF) (Nilsson & Riedel, 2015, 182).

Capacitor consists of two conductive metal plates separated by an insulating material, known as a dielectric. This means that electric charge cannot be transported through the capacitor, instead, applying a voltage to the terminals of the capacitor can displace charge within the dielectric, causing a displacement of current (Figure 1).

This current is indistinguishable from a conduction at the terminals and is proportional to the rate of charge of voltage across the capacitor. The current can be expressed as:

i = C dv / dt (1)

where i is in amperes, C in farads, and v in volts.

Figure 2 shows the passive sign convention based on Equation 1, which the current reference aligns with the voltage drop (current flows from positive sign to negative sign) across the capacitor. However, if the current reference aligns with the voltage rise (current flows from negative sign to positive sign), Equation 1 is written with a minus sign.

Figure 2

1. If the voltage across a capacitor experiences an instantaneous change, an infinite current then occurs, which is physically impossible.

2. If the voltage across the capacitor's terminals remains constant, there will be no current flow through the capacitor, since a conduction current cannot establish itself in the dielectric material; meaning, to have a displacement current, a time-varying voltage must be applied across the terminals.

Thus, a capacitor behaves like an open circuit in the presence of a constant voltage (Nilsson & Riedel, 2015, 183).

From Equation 1, we can rearrange to obtain a voltage equation:

v(t) = 1/C ∫₀^t idτ + v(t₀) (2)

The capacitor energy equation can be expressed as,

w = 1/2 Cv² (3)

Capacitance Connection

1. Series

When capacitors are connected in series (Figure 3), they can be simplified to a single equivalent capacitor. It can be achieved by summing the reciprocals of each individual capacitor's capacitance. The summation will equate to the reciprocal of the equivalent capacitance (Nilsson & Riedel, 2015, 188).

The equivalent capacitance equation can be expressed as:

1/C_eq =1/C₁ +1/C₂ +...+1/C_n (4)

If each capacitor carries an initial voltage, the equivalent capacitor's initial voltage is the sum of the individual capacitors' initial voltages. The voltage equation is obtained through:

v(t) = v₁ (t) + v₂ (t) + ... + v_n (t) (5)

2. Parallel

When capacitors are connected parallel (Figure 4), they can be simplified into an equivalent circuit by summing the capacitance of the individual capacitors.

Figure 4

The equivalent capacitance equation can be expressed as:

C_eq = C₁ + C₂ + ...+ C_n (6)

When capacitors are connected in parallel, they must all have the same voltage. Hence, if an initial voltage is present across the original parallel capacitors, the equivalent capacitance Ceq will also have the same initial voltage.

v(t) = v₁(t) = v₂(t) = ... = v_n(t) (7)

Type of Capacitor

We will now introduce the many different types of capacitors used in industry, each with their own unique characteristics and applications. The most commonly used and inexpensive capacitor found in electronics is the ceramic capacitor (Figure 5). Ceramic capacitors have a small size and high stability, making them ideal for use in high-frequency applications.

Figure 5

For circuits needing higher capacitance than what a ceramic capacitor is capable of, an electrolytic capacitor (Figure 6) is then required. Electrolytic capacitors have a polarized design, meaning that they have both a positive and negative terminal. While able to store more energy in its body, being polarized opens up the risks of breaking if it is installed in the incorrect orientation.

Figure 6

For higher stability and reliability, Tantalum capacitors (Figure 7) are often used, and they are also used in applications where space is limited. Some other benefits to using Tantalum capacitors over ceramic and electrolytic capacitors are that they offer higher performance and greater longevity, but at a greater expense.

Figure 7

Finally, film capacitors (Figure 8) are ideal for circuits that require high-frequency operation and high accuracy.

Figure 8

Application

The popular usage of capacitors in the engineering world is to filter and smooth electrical signals. Any electronic equipment will produce electrical noise in the carrier of various frequency bands. Electronic equipment can also generate radio interference in the high frequency range. Therefore, the capacitor and other electrical passive elements can act as a filter to minimize noise and interference.

In a power supply, the output signal will never be steady. There is always a fluctuation known as ripple. The ripple produces overheating and power losses which jeopardizes the equipment efficiency. Thus, a filter circuit consisting of capacitor or a combination of electrical passive components is used to reduce the ripple at the output.

Conclusion

Each type of capacitor has its unique characteristics and applications, and choosing the right capacitor for a particular application is crucial for the performance and reliability of the circuit. By understanding the properties of different types of capacitors, designers can make informed decisions about the best capacitor to use for a particular application.

References

Ho, J., Jow, T. R., and Boggs, S. (2010). Historical introduction to capacitor technology. IEEE Electrical/Insulation Magazine, 26(1), 20-25. 10.1109/MEI.2010.5383924

Riedel, S. A., and Nilsson, J. W. (2015). Electric Circuits. Pearson.